Question

What is the solution to the system of equations?

8x+16y=−42
−2x+3y=7
​

Answer 1

The solution to the system of equations is x = -27/7 and y = -4/7.

Step-by-step explanation:

To find the solution to the system of equations, we can use the method of substitution or elimination. Let's use the substitution method:

1. Rearrange the first equation to solve for x: 8x = -16y - 42, then divide both sides by 8: x = -2y - 5.5
2. Substitute the value of x into the second equation: -2(-2y - 5.5) + 3y = 7
3. Simplify and solve for y: 4y + 11 + 3y = 7, 7y + 11 = 7, 7y = -4, y = -4/7
4. Substitute the value of y back into the first equation to solve for x: x = -2(-4/7) - 5.5, x = 8/7 - 5.5, x = -27/7

Therefore, the solution to the system of equations is x = -27/7 and y = -4/7.